On Serre's Conjecture over Imaginary Quadratic Fields

Abstract

We study an analog of Serre's conjecture over imaginary quadratic fields. In particular, we ask whether the weight recipe of Buzzard, Diamond and Jarvis will hold in this setting. Using a program written by the author, we provide computational evidence that this is in fact the case. In order to justify the method used in the program, we prove that a modular symbols method will work for arbitrary weights over imaginary quadratic fields.